Question

C
2) A metallic cone in melted to form a cylinder equal radius if the height of the cylinder is 6cm find the height of the cone​

Answer 1

$\bigstar \underline{\underline{\bf Given:-}}$

• A metallic cone in melted to form a cylinder of equal radius.
• Height of cylinder = 6cm.

$\bigstar \underline{\underline{\bf To\ find:-}}$

• Height of cone.

$\bigstar \underline{\underline{\bf Solution:-}}$

Let r=radius ,

=> H =height of cone

=> h = height of cylinder

Given that,

➾r = Radius of solid cone = Radius of solid cylinder.

We know:

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❥Volume of cone =1/3πr²h

❥Volume of cylinder = πr²h

--------------------------------------

Here,

=>Vol of cone = ⅓ πr²H

=>Vol of cylinder = πr²h

Given that Cone is melted to form a cylinder.

So,

➤Volume of cone = Volume of cylinder.

$\\:\implies \sf \frac{1}{3} \cancel{\pi r^2}H=\cancel{\pi r^2}h\\\\:\implies \sf \frac{1}{3} H=h\\\\:\implies \sf \frac{1}{3} H=6 \ \ [Given\ h=6 ]\\\\:\implies \sf H = 6\times 3\\\\:\implies \sf \boxed{\boxed{\bf H=18cm.}}$

Hence,

The height of cone is 18cm.

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➲ Know More:-

✦For cylinder:-

• Lateral surface area = 2πrh.

• Total surface area  = 2πr (h+r)

✦For cone:-

• Lateral surface area = πrl

• Total surface area=πr(l+r)

✦The cone's volume is one third of a cylinder's volume.

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Answer 2

$\bigstar \underline{\underline{\bf Given:-}}$

A metallic cone in melted to form a cylinder of equal radius.

Height of cylinder = 6cm.

$\bigstar \underline{\underline{\bf To\ find:-}}$

Height of cone.

$\bigstar \underline{\underline{\bf Solution:-}}$

Let r=radius ,

=> H =height of cone

=> h = height of cylinder

Given that,

➾r = Radius of solid cone = Radius of solid cylinder.

We know:

--------------------------------------

❥Volume of cone =1/3πr²h

❥Volume of cylinder = πr²h

--------------------------------------

Here,

=>Vol of cone = ⅓ πr²H

=>Vol of cylinder = πr²h

Given that Cone is melted to form a cylinder.

So,

➤Volume of cone = Volume of cylinder.

$\\:\implies \sf \frac{1}{3} \cancel{\pi r^2}H=\cancel{\pi r^2}h\\\\:\implies \sf \frac{1}{3} H=h\\\\:\implies \sf \frac{1}{3} H=6 \ \ [Given\ h=6 ]\\\\:\implies \sf H = 6\times 3\\\\:\implies \sf \boxed{\boxed{\bf H=18cm.}}$

Hence,

The height of cone is 18cm.

----------------------------------

➲ Know More:-

✦For cylinder:-

Lateral surface area = 2πrh.

Total surface area  = 2πr (h+r)

✦For cone:-

Lateral surface area = πrl

Total surface area=πr(l+r)

✦The cone's volume is one third of a cylinder's volume.

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